Compute the total response of a spring-mass system with the following values: k= 1000 N/m, m = 10 kg, subject to a harmonic force of magnitude F0= 100 N and frequency of 8.162 rad/s, and initial conditions given by x0= 0.01 m and v0= 0.01 m/s.
Added by Philip T.
Step 1
- ω_n = sqrt(k/m) = sqrt(1000/10) = 10 rad/s. - Equation: x'' + ω_n^2 x = (F0/m) cos(ωt) with ω = 8.162 rad/s and F0/m = 100/10 = 10. - Particular solution: x_p(t) = A_p cos(ωt), A_p = (F0/m)/(ω_n^2 − ω^2) = 10 /(100 − 8.162^2) = 10 / 33.381756 ≈ 0.299639 m. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Prem Bijarniya and 101 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Adi S.
A mass of 10 kg is attached to a spring of stiffness 0.5 N/m. The mass is given an initial displacement of 0.0 m and an initial velocity of 0.01 m/s. Calculate the natural frequency of the spring-mass system in rad/s and in Hertz. Calculate the response of the mass
A damped spring mass system with values of c = 100 kg/s, m = 100 kg, and k = 910 N/m, is subjected to a force of 10 cos (3t) N. The system is also subjected to initial conditions: x0 = 0.001 m and v0 = 0.02 mm/s. The value of the the amplitude of the transient response form of the system is given by?
Kratika B.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD